Line as source and sink of reactive power

A transmission line has series inductance (which absorbs reactive power) and shunt capacitance (which generates reactive power). Whether the line as a whole is a source or a sink of VArs depends on which of the two is larger, and that depends on the load.

Reactive power generated and absorbed

For a line of length $l$ with reactance $x$ and susceptance $b$ per unit length, at voltage $V$ carrying current $I$:

$$Q_{gen} \approx V^2 b\,l,\qquad Q_{abs} = I^2 x\,l$$

• $Q_{gen}$ depends on voltage, which is nearly constant, so it is almost fixed.
• $Q_{abs}$ depends on $I^2$, so it rises with load.

Three cases

Using the surge impedance $Z_c = \sqrt{L/C}$ and surge impedance loading $SIL = V^2/Z_c$:

 Q net from line
   + |\
     |  \   source (light load)
   0 +----*------------- P
     |    SIL  \
   - |           \  sink (heavy load)

Consequences

• At light load, excess VArs raise receiving-end voltage; shunt reactors are switched in to absorb them.
• At heavy load, the line absorbs VArs and voltage falls; shunt capacitors, SVCs or series capacitors supply VArs.
• Long EHV lines and cables (high $C$) are strong VAr sources at light load; short, heavily loaded lines are VAr sinks.

Example: a 400 kV line with $Z_c = 400\ \Omega$ has SIL = 400 MW. At 200 MW it supplies VArs to the system; at 600 MW it absorbs VArs.